If she is confident and actually getting on your hand then that is very good. I would personally be a little more positive now and actively take her out and handle her so she gets used to the idea that coming out is rather good fun and she will enjoy it. Take the lid off and take the cage so a low soft area where you can really get to know each other. I'm sure she will like her bigger cage but she may become a little skitty again for a while as a cage move can be a bit stressful for them. You sound like a very caring hammy mum and I'm sure she realises this
It isn't unusual for them to be nervous about being taken from an enclosed house which is why we prefer the igloo type that you can just lift up to access the hamster.